Okay, lets boil this down to what it is: This guy is saying that, if elected (and, presumably, when he held a position on the Supreme Court), he will not obey any law that requires equal treatment of men and women.

Therefore, he is saying in advance that he will not obey the law.

Therefore, he is unable to lawfully take an oath of office for anything, much less the head of the executive branch of a Confederate, er…, American state.

Think I’m being hyperbolic?

Will he hire men for positions in government that might require legitimate one-on-one interaction with him?

One would assume so.

Will he hire any woman for any position in government that might require legitimate one-on-one interaction with him?